Question

In: Math

Write the following quadratic function in standard form and then sketch its graph. Clearly mark on...

Write the following quadratic function in standard form and then sketch its graph. Clearly mark on the graph the vertex and all intercepts.

f(x)=-2x^2+6x+15

Note: if you could include step by step explanations so I’ll be able to understand the process and learn this concept that would be great!!

Expert Solution

Given quadratic equation is:

We can write it as:

So given equation is:

On comparing with :

Where (h,k) is vertex of given equation.

SO in given equation vertex of given equation is:

For x intercepts we can equate given equation to zero.

So we will get

So or

So x intercepts are or .

For y intercept we can write x = 0 in given equation

So y intercept is 15.

milcah answered 3 years ago

Part A: Express the quadratic function in standard form (vertex form). ?(?) = 1 − 12?...

Part A: Express the quadratic function in standard form (vertex form). ?(?) = 1 − 12? − 4? 2 Part B: Find the quotient and remainder using synthetic division. ?^4 + 2?^3 − 10? all over ? − 3 Part C: A stone is thrown upward from the top of a building. Its height (in feet) above the ground after t seconds is given by the function ℎ(?) = −16?^2 + 96? + 48. a. What maximum height does the...

Sketch the graph of a function f(x) that satisfies all the given conditions. Clearly label any...

Sketch the graph of a function f(x) that satisfies all the given conditions. Clearly label any asymptotes, extreme values and points of inflection. f(x) is only discontinuous at x = −4. f(x) has a global minimum but no global maximum. f'(x) > 0 only on the intervals (−∞, −4) and (1, 3). f(x) only changes concavity at x = −1 and x = 4. limx→∞ f(x) = 4.

For the following exercises, use the table of values that represent points on the graph of a quadratic function. By determining..

For the following exercises, use the table of values that represent points on the graph of a quadratic function. By determining the vertex and axis of symmetry, find the general form of the equation of the quadratic function.

Clearly state the null and alternative hypotheses Sketch a graph of the rejection region labeled with...

Clearly state the null and alternative hypotheses Sketch a graph of the rejection region labeled with the critical value(s) Calculate the test statistic (showing all work to earn any credit) and p-value (give a range of values for t, chi-square, and F distributions) Write conclusion (3 sentences) Questionnaires were sent to all members of the senior class in a College of Business Administration at a reputable University. One question asked which major within the business program the student had chosen....

Suppose g(x) is in Standard Form of Quadratic with a positive leading coefficient. Answer the following:...

Suppose g(x) is in Standard Form of Quadratic with a positive leading coefficient. Answer the following: A) What is the vertex of g(x)? B) What is the Domain of g(x)? Why? C) What is the Range of g(x)? Why? D) Is the vertex a maximum or minimum? Why?

1. Reduce the quadratic form 2x2 – 6xy + y2 to standard form. Use the new...

1. Reduce the quadratic form 2x2 – 6xy + y2 to standard form. Use the new form to sketch the graph of this quadratic form. What is the angle by which the standard axes are rotated to the standard form orientation 2. find the principal stresses and directions of the stress state given by the matrix 12.5 12.99 12.99 47.5 σ = ksi.

Vertex (−5, 11), opens down. For the following exercises, use the vertex of the graph of the quadratic function and the direction..

For the following exercises, use the vertex of the graph of the quadratic function and the direction the graph opens to find the domain and range of the function.Vertex (−5, 11), opens down.

Sketch the graph of a single function f that satisfies all of the conditions below. (a)...

Sketch the graph of a single function f that satisfies all of the conditions below. (a) f '(x) < 0 on (1,∞), f '(x) > 0 on (−∞,1) (b) f ''(x) > 0 on (−∞,−2) and (2,∞), f ''(x) < 0 on (−2,2) (c) lim x→−∞ f(x) = −2, lim x→∞ f(x) = 0

i. Sketch the velocity vs time graph for the object’s motion described below. Mark all labels...

i. Sketch the velocity vs time graph for the object’s motion described below. Mark all labels and values appropriately. The object at rest starts to move from east to west. • Between 0-4 seconds it moves with an acceleration of 2 ??−2 • Then with a constant velocity for 4-10 seconds. • Finally with a deceleration of 2 ??−2 the object comes to rest. ii. Find the velocity of the object at t= 4 secs and calculate how long the...

1. Sketch the graph of a function that has degree 3, and zeros at -2, +2,...

1. Sketch the graph of a function that has degree 3, and zeros at -2, +2, and +3. Is there only one possible graph? Explain. 2. Find the equation of a 3rd degree function that has a zero of order 3, a vertical stretch of -2, is translated 3 units to the right and 5 units up. (2,21) is a point on the function.